A Theory of Partial Truth for Scientific Statements

Abstract

Scientific representations often combine accurate and inaccurate components, which a single bivalent classification does not distinguish. This paper develops a restricted formal framework for estimating partial factual truth. For fixed content and valuation criteria, the target is adequacy to the facts, independent of the available evidence; its numerical assessment through evidence remains fallible. Quantitative claims are evaluated by normalized discrepancies between asserted and empirically supported values. Admissible finite conjunctions are assessed over a fixed basis of distinct elementary claims using arithmetic or relevance-weighted means. The resulting valuations preserve the contributions from accurate components and are independent of grouping when component counts or total weights are retained. Zero-relevance additions leave the contextual valuation unchanged, but compensation remains possible among components with positive relevance. Worked examples examine admissibility, changes of granularity, measurement indeterminacy, and sensitivity of comparisons to discrepancy scales and relevance weights. An astrophysical application connects the assessment to published observations. The framework applies to selected testable consequences of models and theories, without providing a numerical calculus for arbitrary formulas or a unique method for choosing scales and weights. It permits conditional comparisons of factual adequacy while distinguishing them from confidence, empirical coverage, and convergence toward a complete truth.